
from BP_reward import get_reward
import random
import matplotlib.pyplot as plt
import numpy as np

STUDENT_ID = 810198410
P_SW = 0.8
P_SL = 0.7


def draw_reward_trial_plot(rewards, doctor_name, _color):
    plt.figure(figsize=(8,6))
    plt.plot(range(1,101), rewards, label="reward", color = _color)
    plt.ylabel('sum of rewrads')
    plt.xlabel('trial')
    plt.title('Sum of rewards for Doctor '+ doctor_name + ' approach')
    plt.legend()
    plt.grid()
    plt.show()


def draw_reward_trial_plot_together(rewards, colors):   
    plt.figure(figsize=(8,6))
    plt.plot(range(1,101), rewards[0], label="Doctor A", color = colors[0])
    plt.plot(range(1,101), rewards[1], label="Doctor B", color = colors[1])
    plt.plot(range(1,101), rewards[2], label="Doctor C", color = colors[2])
    plt.ylabel('sum of rewrads')
    plt.xlabel('trial')
    plt.title('Sum of rewards for Doctor A, B, C approach')
    plt.legend()
    plt.grid()
    plt.show()


def doctor_a_single_action(previous_action):
    another_action = 2 if previous_action == 1 else 1  
    reward = get_reward(previous_action, STUDENT_ID)
    next_action = None
    
    if reward > 0:
        if random.random() < P_SW:
            next_action = previous_action
        else:
            next_action = another_action
    else:
        if random.random() > P_SL:
            next_action = previous_action
        else:
            next_action = another_action
            
    return next_action, reward


def doctor_a_approach():
    all_rewards = []
    sum_rewards = 0

    action = random.randint(1, 2)
    for i in range(100):
        action, reward = doctor_a_single_action(action)
        sum_rewards += reward
        all_rewards.append(sum_rewards)
        
    return all_rewards


all_rewards_a = doctor_a_approach()

draw_reward_trial_plot(all_rewards_a, "A", 'b')


def doctor_b_single_action():
    action = random.randint(1, 2) 
    reward = get_reward(action, STUDENT_ID)
    return reward


def doctor_b_approach():
    all_rewards = []
    sum_rewards = 0

    for i in range(100):
        reward = doctor_b_single_action()
        sum_rewards += reward
        all_rewards.append(sum_rewards)
        
    return all_rewards


all_rewards_b = doctor_b_approach()

draw_reward_trial_plot(all_rewards_b, "B", 'r')


def doctor_c_approach():
    all_rewards = []
    sum_rewards = 0

    for i in range(10):
        reward = get_reward(1, STUDENT_ID)
        sum_rewards += reward
        all_rewards.append(sum_rewards)

    for i in range(10):
        reward = get_reward(2, STUDENT_ID)
        sum_rewards += reward
        all_rewards.append(sum_rewards)

    best_action = 1 if all_rewards[9] > (all_rewards[19] - all_rewards[9]) else 2

    for i in range(8):
        for j in range(7):
            reward = get_reward(best_action, STUDENT_ID)
            sum_rewards += reward
            all_rewards.append(sum_rewards)
        for j in range(3):
            action = random.randint(1, 2)
            reward = get_reward(action, STUDENT_ID)
            sum_rewards += reward
            all_rewards.append(sum_rewards)
    
    return all_rewards


all_rewards_c = doctor_c_approach()

draw_reward_trial_plot(all_rewards_c, "C", 'g')


draw_reward_trial_plot_together([all_rewards_a, all_rewards_b, all_rewards_c], ["b", "r", "g"])


def draw_confidence_interval(all_rewards, doctor_name):
    lower_bound = np.percentile(all_rewards, 2.5)
    upper_bound  = np.percentile(all_rewards, 97.5)
    print('Lower bound:',lower_bound)
    print('Upper bound: ',upper_bound)

    all_rewards = np.array(all_rewards)

    plt.figure(figsize=(8,6))
    plt.hist(all_rewards[all_rewards<lower_bound], color='r', label="Outside the confidence interval")
    plt.hist(all_rewards[(all_rewards>=lower_bound)&(all_rewards<=upper_bound)], color='g', label="Inside the confidence interval")
    plt.hist(all_rewards[all_rewards>upper_bound], color='r')
    plt.title("95% confidence interval on the rewards of doctor " + doctor_name +" approach")
    plt.xlabel("reward")
    plt.ylabel("frequency")
    plt.legend()
    plt.grid()
    plt.show()


def repeat_run_of_Q2(number_of_runs):
    for i in range(number_of_runs):
        print("###################################### Run number {} ###########################################".format(i+1))
    
        all_rewards_a = doctor_a_approach()
        draw_reward_trial_plot(all_rewards_a, "A", 'b')
        draw_confidence_interval(all_rewards_a, "A")

        print("======================================================================")

        all_rewards_b = doctor_b_approach()
        draw_reward_trial_plot(all_rewards_b, "B", 'r')
        draw_confidence_interval(all_rewards_b, "B")

        print("======================================================================")

        all_rewards_c = doctor_c_approach()
        draw_reward_trial_plot(all_rewards_c, "C", 'g')
        draw_confidence_interval(all_rewards_c, "C")

        print("======================================================================")

        draw_reward_trial_plot_together([all_rewards_a, all_rewards_b, all_rewards_c], ["b", "r", "g"])


repeat_run_of_Q2(5)

###################################### Run number 1 ###########################################

Lower bound: 5.224535966088991
Upper bound:  84.92092675789833

======================================================================

Lower bound: -29.188213559041497
Upper bound:  12.454773179338611

======================================================================

Lower bound: 1.855277529954893
Upper bound:  95.00612220512443

======================================================================

###################################### Run number 2 ###########################################

Lower bound: -4.650561612760059
Upper bound:  50.9426299106852

======================================================================


repeat_run_of_Q2(20)

###################################### Run number 1 ###########################################

Lower bound: -0.16030239619976117
Upper bound:  72.4382932111568

======================================================================

Lower bound: -24.466559145020142
Upper bound:  9.394860279880707

======================================================================

Lower bound: 6.661509243513117
Upper bound:  119.50572191969015

======================================================================

###################################### Run number 2 ###########################################

Lower bound: 4.88727492037562
Upper bound:  75.94173598150032

======================================================================


def draw_box_plot(doctors_name, rewards):
    fig = plt.figure(figsize =(10, 7))
    plt.boxplot(rewards)
    plt.title("Box plot of doctors approach")
    plt.xlabel('doctors')
    plt.ylabel('reward')
    plt.xticks(range(1, len(doctors_name)+1), doctors_name)
    plt.grid()
    plt.show()


last_reward_a = []
for i in range(10):
    all_rewards = doctor_a_approach()
    last_reward_a.append(all_rewards[-1])
draw_box_plot(["A"], last_reward_a)
    
print("=================================================================================")
    
last_reward_b = []
for i in range(10):
    all_rewards = doctor_b_approach()
    last_reward_b.append(all_rewards[-1])
draw_box_plot(["B"], last_reward_b)
    
print("=================================================================================")
    
last_reward_c = []
for i in range(10):
    all_rewards = doctor_c_approach()
    last_reward_c.append(all_rewards[-1])
draw_box_plot(["C"], last_reward_c)

=================================================================================

=================================================================================


draw_box_plot(["A", "B", "C"], [last_reward_a, last_reward_b, last_reward_c])


reward_1 = 0
reward_2 = 0
r1_more_then_r2 = 0
number_of_runs = 1000000

for i in range(number_of_runs):
    reward_1 += get_reward(1, STUDENT_ID)
    reward_2 += get_reward(2, STUDENT_ID)
    if reward_1 > reward_2 : 
        r1_more_then_r2 += 1
    
print("Total rewards for {} times doing action #1 :".format(number_of_runs), reward_1)
print("Total rewards for {} times doing action #2 :".format(number_of_runs), reward_2)
print("The number of times that reward of action #1 is greater than reward of action #2 :", r1_more_then_r2)

Total rewards for 1000000 times doing action #1 : 1756594.4177150447
Total rewards for 1000000 times doing action #2 : -1403895.107887219
The number of times that reward of action #1 is greater than reward of action #2 : 999999

Table of Contents¶

Packages¶

Question 2¶

Doctor A¶

Doctor B¶

Doctor C¶

Doctor A, B, C¶

Question 3¶

Run 5 times¶

Run 20 times¶

Question 4¶

Run 10 times¶

Question 5¶